Play PSP games on your Android device, at high definition with extra features! PPSSPP is the best, original and only PSP* emulator for Android. It runs a lot of games, but depending on the power of your device all may not run at full speed.

No games are included with this download. Dump your own real PSP games and turn them into .ISO or .CSO files, or simply play free homebrew games, which are available online. Put those in /PSP/GAME on your SD card / USB storage.
Some games that work (not all will run full speed on all devices):
Persona 2, Persona 3 Portable
Dragon Ball Z
Little Big Planet
Burnout Legends, Burnout Dominator
Final Fantasy : Crisis Core
Final Fantasy : Type-0
Monster Hunter 2 Unite and 3: HD Remake
Soul Calibur
Tekken: Dark Resurrection and Tekken 6
Grand Theft Auto LCS / VCS
Lumines
Worms
Wipeout
and many more...